Convective diffusion from channelled laminarly flowing

CONVECTIVE DIFFUSION FROM A CHANNELLED LAMINARLY FLOWING LIQUID... 

The high sensitivity of the Allendoerfer cell makes it of great value in the detection of unstable radicals but, for the study of the kinetics and mechanism of radical decay, the use of a hydrodynamic flow is required. The use of a controlled, defined, and laminar flow of solution past the electrode allows the criteria of mechanism to be established from the solution of the appropriate convective diffusion equation. The uncertain hydrodynamics of earlier in-situ cells employing flow, e.g. Dohrmann [42-45] and Kastening [40, 41], makes such a computational process uncertain and difficult. Similarly, the complex flow between helical electrode surface and internal wall of the quartz cell in the Allendoerfer cell [54, 55] means that the nature of the flow cannot be predicted and so the convective diffusion equation cannot be readily written down, let alone solved Such problems are not experienced by the channel electrode [59], which has well-defined hydrodynamic properties. Compton and Coles [60] adopted the channel electrode as an in-situ ESR cell. 

The Reynolds number in microreaction systems usually ranges from 0.2 to 10. In contrast to the turbulent flow patterns that occur on the macroscale, viscous effects govern the behavior of fluids on the microscale and the flow is always laminar, resulting in a parabolic flow profile. In microfluidic reaction systems, where the characteristic length is usually greater than 10 pm, a continuum description can be used to predict the flow characteristics. This allows commercially written Navier-Stokes solvers such as FEMLAB and FLUENT to model liquid flows in microreaction channels. However, modeling gas flows may require one to take account of boundary sUp conditions (if 10 < Kn < 10 , where Kn is the Knudsen number) and compressibility (if the Mach number Ma is greater than 0.3). Microfluidic reaction systems can be modeled on the basis of the Navier-Stokes equation, in conjunction with convection-diffusion equations for heat and mass transfer, and reaction-kinetic equations. 

A major simplification in the modeling of monolithic channels is to decouple fluid mechanics from the problem by assuming a well-defined velocity profile. In this respect, the laminar flow assumption is likely to be valid since the timescale for viscous diffusion over a transverse length a is much smaller than the one for convection through a channel with length L ... 

---